Question

are you ready for more?
triangle b is a scaled copy of triangle a with scale factor $\frac{1}{2}$.

1. how many times bigger are the side lengths of triangle b when compared with triangle a?
2. imagine you scale triangle b by a scale factor of $\frac{1}{2}$ to get triangle c. how many times bigger will the side lengths of triangle c be when compared with triangle a?
3. triangle b has been scaled once. triangle c has been scaled twice. imagine you scale triangle a $n$ times to get triangle n, always using a scale factor of $\frac{1}{2}$. how many times bigger will the side lengths of triangle n be when compared with triangle a?

5.3: scaling a puzzle
your teacher will give you 2 pieces of a 6 - piece puzzle.

1. if you drew scaled copies of your puzzle pieces using a scale factor of $\frac{1}{2}$, would they be larger or smaller than the original pieces? how do you know?
2. create a scaled copy of each puzzle piece on a blank square, with a scale factor of $\frac{1}{2}$.
3. when everyone in your group is finished, put all 6 of the original puzzle pieces together like this:

1	2	3
4	5	6

Explanation:

Step1: Analyze scaling of Triangle B

Given scale - factor from A to B is $\frac{1}{2}$. This means side - lengths of B are $\frac{1}{2}$ times those of A. So, side - lengths of B are $\frac{1}{2}$ times as big as A's.

Step2: Analyze scaling of Triangle C

Scale from B to C is $\frac{1}{2}$, and from A to B is $\frac{1}{2}$. The combined scale factor from A to C is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$. So, side - lengths of C are $\frac{1}{4}$ times as big as A's.

Step3: Analyze scaling of Triangle N

If we scale triangle A $n$ times with a scale factor of $\frac{1}{2}$ each time, the scale factor from A to N is $(\frac{1}{2})^n$. So, side - lengths of N are $(\frac{1}{2})^n$ times as big as A's.

Step4: Analyze scaled puzzle pieces

If the scale factor is $\frac{1}{2}$, the scaled copies of the puzzle pieces will be smaller. Because a scale factor between 0 and 1 reduces the size of the object.

Answer:

1. $\frac{1}{2}$ times
2. $\frac{1}{4}$ times
3. $(\frac{1}{2})^n$ times
4. Smaller, because the scale factor $\frac{1}{2}<1$.